Convergence in nonlinear systems with a forcing term

• Nápoles, J. E. ^[2] ; Ruiz, A. I. ^[1]
  1. [1] Universidad de Oriente

     Universidad de Oriente

     Venezuela

     
  2. [2] Department of Mathematics and Computation
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 4, Nº. 1, 1997, págs. 1-4
• Idioma: inglés
• DOI: 10.15517/rmta.v4i1.135
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Se considera el problema de la convergencia, cuando t ® +¥ , de las soluciones del sistema(1). Se asume que las funciones a , f y g son de clase C1 para todos los valores de sus argumentos y que además g' (x) > 0, f ' (x) ³ r > 0, 0 < n £ a ' (y) £ N < + ¥ y las funciones a(t) y p (t) son continuas sobre [ 0, +¥ ] con 0 < a £ a(t) £ A < +¥ y p(t) ³ 0.

  • English

    The problem of convergence, as t ® +¥ , of solutions of the system (1) is considered. It is assumed that the functions a , f and g are of class C1 for all values of their arguments, furtermore g' (x) > 0 , f ' (x) ³ r > 0, 0 < n £ a ' (y) £ N < + ¥  and the functions a(t) and p(t) are continuos on [ 0, +¥ ] with 0 < a £ a(t) £ A < +¥ and p(t) ³ 0.

• Referencias bibliográficas
  • Alonso, J.M.; Ortega R. (1995) “Boundedness and global asymptotic stability of a forced oscillator”, Nonlinear Anal. 25: 297–309.
  • Bibikov, Y.N. (1976) “Convergence in Liénard equation with a forcing term”, Vestnik LGU 7: 73–75 (russian).
  • Nápoles, J.E. “On the boundedness and global stability of solutions of a system of differential equations”, to appear in Rev. Ciencias Matemáticas,...
  • Nápoles, J.E. “On the global stability of non-autonomous systems”, submited for publication.
  • Nazarov, E.A. (1977) “The coming together of the solutions of Liénard’s equation” , Differencial ’nye Uravnenija 13: 1792–1795 (russian).
  • Opial, Z. (1960-61) “Sur un théorème de C.E. Langenhop et G. Seifert ”, Ann. Polon. Math.9: 145–155.
  • Repilado, J.A.; J.E. Nápoles. “On the convergence of solutions of a bidimensional system to unique periodic solution ”, submited for publication.
  • Ruiz, A. (1993) “On the convergence of solutions of system x′ = h(y) − f(x), y′ = −g(x) + p(t) to a bounded solution ”, Rev. Ciencias...